50.17.13 problem 2(a) solving using series

Internal problem ID [8084]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 4. Power Series Solutions and Special Functions. Section 4.2. Series Solutions of First-Order Differential Equations Page 162
Problem number : 2(a) solving using series
Date solved : Monday, January 27, 2025 at 03:43:25 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }&=y \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 12

Order:=8; 
dsolve(x*diff(y(x),x)=y(x),y(x),type='series',x=0);
 

\[ y = c_{1} x +O\left (x^{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 7

AsymptoticDSolveValue[x*D[y[x],x]==y[x],y[x],{x,0,"8"-1}]
 

\[ y(x)\to c_1 x \]